Status 53 and 51 in IDoc Processing

For IDoc processing, does status 53 and 51 have a significant meaning? What does the idoc require in order to have the application document posted or not?

e.g. I'm thinking that, status 51 means there's a lack in configuration while status 53 means that there's a conflicting/difference in value from the transferred data in the idoc from a reference Master Data.

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The IDOC status let's you know if the IDOC is processed successfully or not including error types depending on the status. Status 53 is usually good news, which means the IDOC is processed successfully and the corresponding document is updated. You get status 51 when the IDOC fails to get posted successfully. The message can be found in 'Status Text' field under the IDOC. The requirements for correct posting is quite large, which starts from correct connection to the broker or other system, valid and correct partner profile, segment data structure maintenance and definitely valid incoming data.

Status 51 means the IDOC has not been successfully posted. It has
error(s)--- manual processing will be required. Whereas status 53 means
the idoc has been successfully posted. That is the little knowledge I
have. Any other thoughts?

Status 53 means the document posted successfully. Status 51 means it failed. Why it failed depends on the IDoc, the document it's trying to post, and the data it's carrying but 51 is an application failure.